In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding ε k of an orthogonal Grassmannian ∆k. In particular, we determine some of the parameters of the codes arising from the projective system determined by ε k (∆k). We also study special sets of points of ∆k which are met by any line of ∆k in at most 2 points and we show that their imag...

We give a characterization of the ‘special linear groups’ T (Ψ,W ) as linear groups generated by a non-degenerate class Σ of abstract root groups such that the elements of A ∈ Σ are transvections.

In this paper we present a generic projective interior point algorithm for linear programming which includes modiied versions of Karmarkar's original algorithm and most other projective algorithms that have been proposed as special cases. We show that this class of algorithms has a worst case iteration bound of O(p nL) and is closely related to the class of potential reduction interior point me...

In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group L2(49). As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to L2(49) except L2(49) · 22. Also, we prove that if M is an almost simple group relate...